// See LICENSE for license details.

#define R 1000
#define C 1000
#define NNZ 10004
const double val[10004] = {
  658,
  279,
  587,
  255,
  359,
  844,
  905,
  456,
  897,
  837,
  652,
  398,
  885,
  21,
  669,
  738,
  365,
  928,
  713,
  771,
  536,
  987,
  917,
  823,
  544,
  40,
  80,
  636,
  263,
  929,
  757,
  677,
  151,
  500,
  875,
  720,
  205,
  292,
  859,
  980,
  97,
  608,
  813,
  840,
  397,
  765,
  294,
  718,
  751,
  7,
  482,
  166,
  653,
  172,
  187,
  79,
  228,
  857,
  540,
  760,
  509,
  190,
  396,
  765,
  37,
  85,
  866,
  981,
  999,
  793,
  921,
  664,
  208,
  856,
  528,
  782,
  318,
  170,
  521,
  691,
  726,
  996,
  947,
  326,
  825,
  77,
  823,
  752,
  266,
  834,
  196,
  58,
  430,
  764,
  807,
  568,
  665,
  583,
  178,
  250,
  273,
  654,
  487,
  504,
  729,
  338,
  866,
  981,
  852,
  842,
  785,
  13,
  588,
  44,
  432,
  408,
  374,
  761,
  653,
  752,
  684,
  6,
  357,
  703,
  447,
  966,
  457,
  738,
  646,
  646,
  217,
  522,
  839,
  417,
  506,
  801,
  233,
  929,
  487,
  353,
  660,
  751,
  738,
  512,
  566,
  130,
  61,
  128,
  698,
  467,
  362,
  867,
  639,
  289,
  371,
  427,
  650,
  16,
  878,
  967,
  369,
  517,
  161,
  330,
  294,
  396,
  606,
  638,
  171,
  602,
  531,
  14,
  968,
  15,
  193,
  225,
  863,
  171,
  254,
  714,
  256,
  873,
  353,
  35,
  910,
  849,
  658,
  546,
  389,
  239,
  355,
  540,
  494,
  968,
  319,
  590,
  608,
  445,
  806,
  51,
  117,
  401,
  314,
  280,
  334,
  44,
  17,
  107,
  108,
  650,
  807,
  385,
  748,
  942,
  719,
  110,
  630,
  559,
  717,
  375,
  963,
  45,
  403,
  476,
  408,
  732,
  87,
  874,
  635,
  119,
  190,
  949,
  777,
  201,
  503,
  658,
  777,
  564,
  830,
  122,
  929,
  68,
  11,
  354,
  395,
  213,
  766,
  40,
  995,
  577,
  514,
  568,
  56,
  439,
  91,
  148,
  612,
  717,
  157,
  538,
  682,
  190,
  571,
  847,
  275,
  190,
  824,
  985,
  29,
  426,
  173,
  898,
  297,
  156,
  936,
  1,
  455,
  812,
  173,
  131,
  376,
  947,
  596,
  783,
  800,
  361,
  798,
  598,
  710,
  86,
  149,
  457,
  129,
  437,
  352,
  933,
  320,
  709,
  167,
  793,
  46,
  49,
  305,
  704,
  577,
  855,
  336,
  978,
  206,
  662,
  230,
  93,
  898,
  368,
  422,
  689,
  351,
  87,
  465,
  576,
  33,
  884,
  675,
  548,
  116,
  730,
  385,
  483,
  340,
  809,
  938,
  342,
  576,
  887,
  479,
  455,
  820,
  521,
  320,
  488,
  506,
  591,
  901,
  505,
  525,
  5,
  133,
  705,
  561,
  285,
  95,
  918,
  410,
  578,
  347,
  375,
  735,
  624,
  491,
  494,
  931,
  655,
  819,
  883,
  328,
  527,
  194,
  580,
  584,
  837,
  700,
  681,
  249,
  643,
  958,
  363,
  316,
  397,
  638,
  261,
  459,
  960,
  636,
  458,
  84,
  797,
  696,
  782,
  831,
  419,
  393,
  649,
  312,
  811,
  703,
  70,
  688,
  285,
  39,
  617,
  935,
  495,
  392,
  143,
  734,
  166,
  406,
  464,
  732,
  709,
  379,
  143,
  527,
  514,
  709,
  130,
  965,
  632,
  448,
  836,
  62,
  567,
  600,
  520,
  519,
  16,
  394,
  705,
  438,
  548,
  696,
  140,
  573,
  509,
  968,
  935,
  165,
  868,
  577,
  451,
  865,
  304,
  777,
  828,
  147,
  704,
  821,
  641,
  783,
  376,
  757,
  391,
  170,
  592,
  235,
  920,
  846,
  683,
  249,
  697,
  253,
  386,
  244,
  889,
  607,
  768,
  88,
  836,
  259,
  945,
  33,
  352,
  70,
  83,
  996,
  791,
  18,
  599,
  488,
  43,
  582,
  993,
  692,
  841,
  558,
  530,
  350,
  187,
  295,
  215,
  869,
  593,
  385,
  722,
  724,
  282,
  681,
  534,
  788,
  836,
  378,
  825,
  93,
  539,
  120,
  794,
  384,
  798,
  505,
  833,
  27,
  181,
  951,
  966,
  498,
  375,
  22,
  545,
  62,
  816,
  119,
  712,
  813,
  783,
  655,
  832,
  143,
  501,
  519,
  43,
  760,
  17,
  896,
  96,
  390,
  121,
  458,
  736,
  649,
  227,
  778,
  283,
  657,
  434,
  214,
  123,
  929,
  548,
  206,
  993,
  463,
  824,
  369,
  260,
  868,
  645,
  857,
  184,
  198,
  349,
  652,
  522,
  23,
  208,
  968,
  290,
  770,
  109,
  978,
  513,
  298,
  675,
  306,
  866,
  927,
  822,
  495,
  653,
  134,
  702,
  147,
  366,
  947,
  65,
  586,
  412,
  638,
  760,
  541,
  118,
  551,
  574,
  85,
  736,
  999,
  917,
  478,
  35,
  629,
  963,
  898,
  826,
  113,
  298,
  606,
  568,
  152,
  926,
  277,
  984,
  549,
  279,
  839,
  348,
  672,
  278,
  94,
  455,
  590,
  843,
  85,
  222,
  901,
  621,
  30,
  880,
  914,
  27,
  974,
  399,
  873,
  968,
  870,
  479,
  696,
  964,
  929,
  499,
  121,
  812,
  933,
  799,
  506,
  412,
  712,
  791,
  426,
  835,
  488,
  910,
  522,
  332,
  967,
  380,
  61,
  5,
  282,
  119,
  22,
  136,
  436,
  730,
  341,
  687,
  371,
  19,
  893,
  20,
  327,
  221,
  221,
  966,
  354,
  198,
  985,
  56,
  305,
  691,
  980,
  12,
  790,
  64,
  484,
  621,
  214,
  332,
  898,
  898,
  318,
  416,
  445,
  350,
  317,
  336,
  714,
  788,
  541,
  890,
  42,
  111,
  596,
  164,
  424,
  448,
  666,
  362,
  429,
  617,
  910,
  917,
  970,
  526,
  321,
  551,
  481,
  83,
  46,
  146,
  569,
  856,
  85,
  192,
  724,
  378,
  299,
  13,
  422,
  411,
  552,
  569,
  100,
  849,
  484,
  906,
  47,
  532,
  742,
  415,
  228,
  897,
  715,
  807,
  329,
  244,
  312,
  903,
  758,
  34,
  172,
  18,
  917,
  700,
  108,
  611,
  567,
  616,
  572,
  174,
  925,
  553,
  903,
  268,
  544,
  998,
  708,
  133,
  717,
  584,
  517,
  608,
  680,
  597,
  316,
  470,
  764,
  530,
  221,
  405,
  133,
  406,
  506,
  56,
  458,
  721,
  935,
  356,
  130,
  99,
  395,
  117,
  34,
  881,
  231,
  214,
  248,
  458,
  246,
  632,
  471,
  279,
  385,
  594,
  855,
  305,
  30,
  542,
  144,
  509,
  548,
  364,
  171,
  386,
  382,
  616,
  997,
  28,
  361,
  855,
  449,
  992,
  956,
  439,
  569,
  383,
  523,
  852,
  337,
  112,
  24,
  902,
  352,
  542,
  231,
  664,
  411,
  457,
  572,
  52,
  760,
  88,
  907,
  345,
  284,
  636,
  219,
  975,
  713,
  231,
  888,
  49,
  624,
  179,
  579,
  401,
  694,
  984,
  905,
  673,
  414,
  773,
  165,
  349,
  436,
  128,
  186,
  487,
  17,
  552,
  833,
  98,
  424,
  791,
  220,
  352,
  75,
  470,
  405,
  679,
  939,
  792,
  653,
  142,
  226,
  208,
  629,
  429,
  55,
  455,
  362,
  210,
  765,
  693,
  113,
  656,
  824,
  441,
  191,
  50,
  957,
  99,
  27,
  582,
  461,
  279,
  299,
  492,
  678,
  452,
  640,
  349,
  758,
  298,
  903,
  361,
  333,
  339,
  60,
  824,
  773,
  184,
  621,
  66,
  49,
  228,
  608,
  523,
  591,
  533,
  234,
  566,
  291,
  646,
  93,
  42,
  810,
  154,
  846,
  426,
  32,
  828,
  360,
  917,
  182,
  50,
  40,
  182,
  19,
  127,
  614,
  951,
  662,
  591,
  140,
  110,
  685,
  549,
  6,
  346,
  766,
  689,
  743,
  414,
  135,
  61,
  548,
  363,
  915,
  462,
  526,
  405,
  524,
  192,
  754,
  796,
  616,
  98,
  341,
  786,
  778,
  929,
  6,
  388,
  293,
  513,
  148,
  298,
  311,
  29,
  456,
  960,
  560,
  895,
  121,
  511,
  141,
  732,
  762,
  774,
  261,
  287,
  314,
  801,
  320,
  173,
  616,
  356,
  783,
  256,
  129,
  513,
  212,
  293,
  168,
  813,
  279,
  65,
  784,
  360,
  921,
  320,
  177,
  923,
  385,
  142,
  380,
  772,
  929,
  718,
  277,
  61,
  620,
  575,
  772,
  356,
  414,
  775,
  392,
  523,
  760,
  192,
  905,
  606,
  134,
  695,
  784,
  540,
  63,
  939,
  941,
  887,
  217,
  290,
  893,
  206,
  662,
  63,
  102,
  74,
  943,
  288,
  8,
  254,
  131,
  420,
  841,
  79,
  139,
  362,
  221,
  915,
  6,
  28,
  417,
  846,
  996,
  794,
  522,
  391,
  513,
  715,
  87,
  449,
  801,
  823,
  16,
  485,
  874,
  8,
  601,
  885,
  146,
  886,
  318,
  235,
  390,
  561,
  869,
  640,
  860,
  433,
  651,
  145,
  149,
  682,
  612,
  580,
  946,
  572,
  155,
  736,
  898,
  774,
  81,
  882,
  286,
  362,
  982,
  788,
  658,
  452,
  889,
  688,
  384,
  948,
  342,
  402,
  777,
  403,
  547,
  123,
  187,
  394,
  470,
  978,
  234,
  461,
  127,
  349,
  476,
  927,
  837,
  997,
  494,
  167,
  920,
  911,
  84,
  432,
  339,
  87,
  841,
  535,
  972,
  671,
  395,
  445,
  681,
  494,
  737,
  492,
  96,
  84,
  261,
  871,
  91,
  696,
  960,
  346,
  430,
  796,
  326,
  272,
  982,
  25,
  927,
  923,
  528,
  924,
  215,
  789,
  691,
  898,
  811,
  189,
  284,
  856,
  200,
  278,
  436,
  354,
  114,
  978,
  648,
  797,
  437,
  916,
  220,
  449,
  740,
  179,
  484,
  470,
  332,
  178,
  65,
  807,
  860,
  180,
  421,
  148,
  563,
  253,
  691,
  121,
  837,
  851,
  341,
  948,
  563,
  635,
  780,
  148,
  567,
  713,
  118,
  877,
  505,
  519,
  975,
  504,
  745,
  190,
  958,
  134,
  898,
  723,
  546,
  781,
  46,
  760,
  530,
  572,
  163,
  227,
  886,
  408,
  586,
  4,
  901,
  233,
  753,
  720,
  203,
  575,
  748,
  443,
  207,
  838,
  492,
  290,
  223,
  256,
  715,
  830,
  432,
  97,
  99,
  477,
  725,
  574,
  91,
  746,
  731,
  615,
  629,
  437,
  320,
  843,
  559,
  13,
  902,
  779,
  564,
  689,
  207,
  599,
  726,
  598,
  606,
  148,
  58,
  115,
  536,
  319,
  279,
  944,
  485,
  699,
  948,
  13,
  895,
  766,
  582,
  559,
  998,
  250,
  788,
  869,
  877,
  23,
  647,
  488,
  164,
  845,
  344,
  545,
  307,
  991,
  0,
  805,
  152,
  412,
  534,
  323,
  614,
  415,
  865,
  847,
  210,
  743,
  122,
  943,
  594,
  320,
  268,
  154,
  253,
  816,
  347,
  768,
  953,
  982,
  606,
  131,
  813,
  92,
  339,
  5,
  707,
  517,
  526,
  469,
  537,
  89,
  141,
  537,
  557,
  190,
  659,
  87,
  659,
  401,
  367,
  414,
  460,
  34,
  96,
  895,
  740,
  694,
  352,
  537,
  592,
  877,
  137,
  922,
  915,
  99,
  216,
  969,
  716,
  44,
  869,
  856,
  853,
  352,
  556,
  216,
  426,
  231,
  259,
  172,
  67,
  694,
  488,
  311,
  712,
  767,
  279,
  962,
  265,
  615,
  141,
  454,
  711,
  384,
  452,
  135,
  90,
  391,
  787,
  665,
  528,
  296,
  824,
  820,
  455,
  885,
  301,
  155,
  647,
  6,
  973,
  627,
  663,
  922,
  969,
  799,
  698,
  523,
  404,
  784,
  422,
  128,
  103,
  233,
  601,
  812,
  281,
  600,
  336,
  11,
  743,
  288,
  925,
  181,
  228,
  508,
  308,
  3,
  141,
  711,
  602,
  71,
  868,
  255,
  307,
  24,
  862,
  567,
  134,
  74,
  755,
  947,
  111,
  812,
  42,
  295,
  650,
  859,
  78,
  128,
  462,
  308,
  290,
  372,
  166,
  111,
  364,
  469,
  591,
  127,
  56,
  840,
  758,
  781,
  756,
  548,
  658,
  412,
  851,
  134,
  233,
  432,
  257,
  138,
  210,
  184,
  986,
  51,
  806,
  442,
  711,
  243,
  571,
  861,
  550,
  111,
  798,
  138,
  316,
  746,
  549,
  276,
  458,
  866,
  335,
  334,
  178,
  191,
  473,
  452,
  764,
  487,
  525,
  273,
  457,
  902,
  888,
  519,
  203,
  891,
  497,
  998,
  535,
  382,
  673,
  787,
  112,
  846,
  836,
  898,
  681,
  607,
  546,
  863,
  639,
  896,
  281,
  845,
  305,
  410,
  835,
  985,
  245,
  781,
  208,
  337,
  248,
  205,
  264,
  198,
  305,
  665,
  351,
  609,
  186,
  444,
  589,
  130,
  292,
  668,
  617,
  611,
  111,
  80,
  9,
  267,
  275,
  135,
  201,
  926,
  789,
  835,
  221,
  290,
  297,
  93,
  437,
  892,
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  506,
  127,
  844,
  749,
  674,
  845,
  529,
  865,
  635,
  791,
  776,
  334,
  136,
  342,
  593,
  512,
  660,
  640,
  787,
  139,
  544,
  181,
  43,
  46,
  413,
  337,
  854,
  986,
  815,
  121,
  877,
  294,
  218,
  4,
  136,
  225,
  766,
  992,
  910,
  530,
  646,
  213,
  695,
  271,
  967,
  986,
  628,
  777,
  180,
  866,
  599,
  664,
  46,
  994,
  396,
  56,
  256,
  739,
  481,
  608,
  360,
  134,
  970,
  282,
  898,
  417,
  948,
  956,
  230,
  884,
  748,
  74,
  938,
  224,
  920,
  974,
  475,
  405,
  442,
  630,
  596,
  118,
  398,
  439,
  969,
  188,
  169,
  251,
  630,
  835,
  480,
  557,
  904,
  461,
  371,
  885,
  197,
  305,
  678,
  12,
  663,
  960,
  311,
  877,
  747,
  20,
  271,
  622,
  48,
  621,
  135,
  59,
  179,
  377,
  684,
  861,
  760,
  38,
  780,
  91,
  18,
  23,
  432,
  37,
  443,
  450,
  508,
  193,
  960,
  986,
  761,
  605,
  788,
  86,
  436,
  23,
  581,
  605,
  128,
  84,
  979,
  732,
  230,
  787,
  836,
  261,
  677,
  117,
  292,
  477,
  388,
  20,
  962,
  707,
  979,
  933,
  662,
  112,
  234,
  771,
  167,
  31,
  673,
  42,
  705,
  675,
  151,
  452,
  875,
  655,
  399,
  59,
  702,
  502,
  444,
  892,
  290,
  856,
  53,
  260,
  19,
  221,
  987,
  330,
  80,
  665,
  551,
  377,
  540,
  188,
  920,
  680,
  133,
  77,
  466,
  439,
  258,
  570,
  659,
  56,
  10,
  615,
  504,
  336,
  655,
  720,
  156,
  289,
  354,
  637,
  184,
  853,
  944,
  177,
  973,
  177,
  537,
  934,
  78,
  267,
  209,
  898,
  115,
  986,
  920,
  926,
  393,
  217,
  204,
  312,
  989,
  655,
  214,
  47,
  231,
  278,
  866,
  734,
  707,
  605,
  208,
  232,
  506,
  116,
  383,
  662,
  151,
  92,
  785,
  431,
  614,
  585,
  682,
  781,
  343,
  590,
  458,
  232,
  360,
  187,
  18,
  769,
  704,
  620,
  67,
  109,
  88,
  353,
  401,
  228,
  508,
  406,
  255,
  989,
  151,
  702,
  277,
  376,
  381,
  409,
  932,
  31,
  761,
  783,
  233,
  154,
  871,
  55,
  648,
  5,
  12,
  465,
  96,
  904,
  169,
  325,
  428,
  572,
  47,
  78,
  258,
  525,
  276,
  502,
  972,
  488,
  763,
  798,
  973,
  186,
  490,
  362,
  205,
  154,
  245,
  784,
  493,
  76,
  975,
  459,
  598,
  227,
  161,
  752,
  243,
  858,
  931,
  996,
  543,
  488,
  560,
  240,
  49,
  318,
  374,
  914,
  52,
  693,
  762,
  329,
  691,
  193,
  122,
  925,
  577,
  748,
  236,
  8,
  591,
  640,
  61,
  77,
  295,
  117,
  323,
  732,
  493,
  811,
  67,
  694,
  158,
  589,
  247,
  115,
  184,
  682,
  927,
  918,
  353,
  217,
  904,
  834,
  107,
  728,
  683,
  908,
  596,
  721,
  44,
  412,
  780,
  882,
  682,
  497,
  832,
  559,
  126,
  303,
  100,
  214,
  829,
  344,
  654,
  679,
  336,
  148,
  213,
  982,
  859,
  558,
  855,
  999,
  698,
  38,
  490,
  340,
  846,
  852,
  26,
  942,
  575,
  383,
  1,
  198,
  836,
  570,
  893,
  950,
  7,
  527,
  628,
  753,
  660,
  180,
  354,
  819,
  775,
  271,
  187,
  374,
  532,
  374,
  900
};
const int idx[10004] = {
  13,
  111,
  124,
  218,
  316,
  502,
  34,
  119,
  167,
  180,
  186,
  346,
  511,
  543,
  755,
  788,
  833,
  929,
  46,
  109,
  154,
  220,
  248,
  448,
  509,
  517,
  530,
  557,
  639,
  643,
  720,
  137,
  189,
  424,
  480,
  570,
  642,
  849,
  896,
  968,
  117,
  136,
  208,
  248,
  347,
  410,
  433,
  515,
  747,
  144,
  148,
  375,
  405,
  444,
  532,
  788,
  808,
  987,
  110,
  112,
  403,
  415,
  596,
  612,
  669,
  794,
  851,
  80,
  285,
  288,
  433,
  500,
  628,
  982,
  999,
  57,
  237,
  252,
  304,
  469,
  600,
  609,
  621,
  741,
  798,
  251,
  322,
  369,
  374,
  376,
  507,
  623,
  666,
  669,
  677,
  707,
  823,
  919,
  63,
  187,
  266,
  360,
  396,
  439,
  459,
  526,
  623,
  804,
  857,
  881,
  948,
  160,
  165,
  226,
  446,
  538,
  585,
  624,
  866,
  975,
  979,
  18,
  54,
  151,
  180,
  230,
  298,
  480,
  678,
  688,
  696,
  742,
  757,
  889,
  979,
  100,
  245,
  513,
  925,
  162,
  413,
  427,
  588,
  645,
  807,
  853,
  194,
  313,
  339,
  466,
  539,
  581,
  732,
  791,
  832,
  927,
  954,
  962,
  966,
  42,
  45,
  138,
  141,
  239,
  338,
  584,
  696,
  912,
  929,
  269,
  352,
  443,
  463,
  896,
  962,
  60,
  92,
  273,
  568,
  591,
  851,
  38,
  77,
  281,
  362,
  544,
  614,
  651,
  836,
  871,
  873,
  45,
  61,
  140,
  153,
  234,
  439,
  472,
  509,
  588,
  675,
  760,
  777,
  178,
  198,
  248,
  517,
  566,
  679,
  700,
  289,
  455,
  602,
  695,
  711,
  853,
  923,
  179,
  199,
  214,
  280,
  343,
  405,
  435,
  504,
  898,
  910,
  939,
  130,
  219,
  296,
  445,
  508,
  634,
  763,
  918,
  922,
  978,
  87,
  285,
  614,
  667,
  679,
  739,
  834,
  192,
  347,
  549,
  557,
  724,
  764,
  928,
  929,
  976,
  17,
  283,
  413,
  429,
  612,
  683,
  707,
  725,
  743,
  833,
  856,
  165,
  267,
  304,
  361,
  397,
  410,
  570,
  683,
  766,
  788,
  849,
  882,
  885,
  30,
  58,
  221,
  254,
  453,
  457,
  470,
  674,
  687,
  745,
  809,
  819,
  55,
  121,
  231,
  538,
  604,
  718,
  768,
  960,
  71,
  77,
  104,
  186,
  205,
  234,
  456,
  467,
  579,
  682,
  733,
  767,
  947,
  66,
  86,
  157,
  290,
  422,
  441,
  473,
  560,
  607,
  640,
  682,
  888,
  37,
  296,
  439,
  629,
  642,
  733,
  824,
  917,
  969,
  4,
  25,
  580,
  622,
  636,
  666,
  672,
  732,
  802,
  921,
  943,
  130,
  194,
  245,
  273,
  323,
  344,
  603,
  740,
  795,
  974,
  189,
  422,
  445,
  446,
  831,
  905,
  912,
  36,
  60,
  218,
  428,
  455,
  627,
  743,
  796,
  801,
  903,
  136,
  152,
  166,
  352,
  364,
  369,
  382,
  466,
  521,
  577,
  665,
  746,
  910,
  294,
  345,
  445,
  645,
  686,
  718,
  757,
  762,
  796,
  817,
  832,
  836,
  997,
  127,
  258,
  259,
  449,
  541,
  643,
  665,
  756,
  817,
  854,
  870,
  89,
  134,
  188,
  362,
  408,
  531,
  566,
  816,
  127,
  170,
  302,
  336,
  426,
  434,
  601,
  708,
  774,
  780,
  900,
  935,
  377,
  469,
  618,
  650,
  790,
  809,
  78,
  253,
  340,
  382,
  586,
  673,
  684,
  282,
  354,
  363,
  398,
  636,
  655,
  729,
  885,
  911,
  10,
  175,
  195,
  229,
  273,
  339,
  380,
  531,
  660,
  681,
  794,
  800,
  236,
  416,
  646,
  679,
  685,
  885,
  7,
  116,
  299,
  481,
  702,
  747,
  922,
  64,
  153,
  374,
  391,
  532,
  558,
  602,
  655,
  662,
  804,
  847,
  867,
  998,
  45,
  66,
  97,
  106,
  236,
  240,
  247,
  453,
  641,
  646,
  711,
  712,
  715,
  855,
  906,
  923,
  37,
  65,
  122,
  331,
  578,
  589,
  610,
  139,
  293,
  354,
  395,
  430,
  486,
  589,
  614,
  661,
  699,
  846,
  910,
  18,
  53,
  78,
  234,
  296,
  690,
  828,
  923,
  87,
  115,
  156,
  161,
  173,
  201,
  400,
  474,
  501,
  526,
  782,
  861,
  63,
  271,
  427,
  552,
  590,
  657,
  920,
  41,
  194,
  281,
  571,
  640,
  681,
  696,
  301,
  306,
  514,
  553,
  560,
  641,
  683,
  762,
  812,
  818,
  876,
  904,
  932,
  978,
  38,
  62,
  98,
  103,
  370,
  390,
  531,
  559,
  693,
  813,
  924,
  943,
  955,
  973,
  13,
  40,
  62,
  75,
  396,
  419,
  615,
  773,
  968,
  989,
  150,
  183,
  241,
  261,
  407,
  476,
  492,
  524,
  541,
  863,
  994,
  156,
  195,
  197,
  278,
  457,
  467,
  610,
  621,
  956,
  49,
  343,
  454,
  477,
  572,
  600,
  700,
  759,
  804,
  923,
  92,
  194,
  455,
  842,
  968,
  160,
  211,
  461,
  463,
  467,
  622,
  854,
  972,
  333,
  469,
  563,
  571,
  639,
  838,
  977,
  18,
  105,
  133,
  258,
  572,
  720,
  804,
  851,
  930,
  19,
  139,
  158,
  301,
  354,
  407,
  589,
  726,
  846,
  904,
  26,
  54,
  155,
  212,
  216,
  418,
  534,
  647,
  792,
  862,
  889,
  101,
  216,
  228,
  396,
  470,
  473,
  592,
  706,
  799,
  913,
  922,
  98,
  324,
  524,
  672,
  685,
  856,
  213,
  224,
  228,
  300,
  395,
  604,
  631,
  651,
  835,
  944,
  289,
  574,
  613,
  657,
  671,
  748,
  763,
  768,
  815,
  843,
  908,
  74,
  79,
  203,
  218,
  245,
  249,
  390,
  548,
  616,
  804,
  986,
  49,
  196,
  585,
  591,
  608,
  728,
  750,
  810,
  836,
  920,
  980,
  38,
  41,
  93,
  94,
  320,
  360,
  502,
  555,
  729,
  742,
  814,
  984,
  89,
  131,
  499,
  677,
  825,
  846,
  919,
  966,
  17,
  37,
  121,
  168,
  560,
  585,
  691,
  788,
  892,
  925,
  951,
  995,
  13,
  69,
  124,
  229,
  308,
  554,
  643,
  668,
  717,
  747,
  813,
  814,
  864,
  298,
  327,
  386,
  425,
  586,
  600,
  725,
  730,
  832,
  12,
  38,
  94,
  150,
  175,
  501,
  538,
  552,
  571,
  606,
  624,
  650,
  686,
  728,
  157,
  605,
  630,
  713,
  784,
  850,
  954,
  181,
  234,
  610,
  612,
  661,
  663,
  677,
  688,
  726,
  809,
  818,
  67,
  77,
  164,
  193,
  214,
  345,
  352,
  551,
  696,
  919,
  994,
  12,
  311,
  404,
  454,
  473,
  521,
  581,
  651,
  677,
  717,
  850,
  873,
  880,
  892,
  945,
  54,
  138,
  210,
  219,
  248,
  413,
  480,
  491,
  639,
  652,
  773,
  807,
  824,
  962,
  79,
  211,
  499,
  560,
  561,
  759,
  774,
  800,
  865,
  35,
  146,
  619,
  746,
  754,
  81,
  237,
  258,
  388,
  477,
  658,
  704,
  712,
  781,
  109,
  720,
  758,
  98,
  209,
  252,
  311,
  410,
  532,
  611,
  656,
  722,
  772,
  822,
  828,
  912,
  980,
  95,
  107,
  167,
  287,
  289,
  303,
  441,
  446,
  580,
  600,
  630,
  632,
  658,
  682,
  847,
  92,
  137,
  177,
  238,
  262,
  324,
  438,
  479,
  534,
  539,
  689,
  846,
  956,
  962,
  200,
  496,
  521,
  656,
  714,
  785,
  814,
  857,
  184,
  204,
  455,
  702,
  754,
  803,
  887,
  928,
  993,
  42,
  51,
  189,
  204,
  358,
  572,
  601,
  665,
  867,
  71,
  108,
  208,
  243,
  263,
  314,
  359,
  418,
  482,
  556,
  680,
  945,
  958,
  964,
  97,
  200,
  202,
  223,
  230,
  428,
  447,
  537,
  574,
  635,
  663,
  728,
  737,
  858,
  861,
  930,
  71,
  84,
  85,
  196,
  199,
  242,
  513,
  761,
  48,
  98,
  127,
  194,
  233,
  283,
  334,
  420,
  627,
  632,
  931,
  34,
  82,
  176,
  197,
  217,
  235,
  237,
  358,
  462,
  947,
  10,
  178,
  265,
  350,
  396,
  468,
  539,
  586,
  612,
  628,
  644,
  791,
  40,
  234,
  292,
  299,
  375,
  396,
  410,
  429,
  728,
  36,
  360,
  475,
  562,
  962,
  5,
  60,
  169,
  509,
  558,
  594,
  613,
  648,
  654,
  726,
  769,
  773,
  777,
  40,
  49,
  403,
  446,
  524,
  548,
  730,
  774,
  938,
  978,
  997,
  221,
  248,
  407,
  447,
  585,
  756,
  824,
  894,
  972,
  121,
  189,
  364,
  537,
  563,
  179,
  328,
  344,
  692,
  711,
  750,
  760,
  780,
  810,
  929,
  942,
  106,
  336,
  551,
  616,
  640,
  654,
  726,
  890,
  74,
  200,
  233,
  254,
  382,
  396,
  895,
  971,
  283,
  614,
  898,
  87,
  122,
  172,
  255,
  324,
  383,
  498,
  525,
  699,
  817,
  825,
  3,
  41,
  104,
  280,
  399,
  617,
  641,
  769,
  789,
  817,
  891,
  937,
  143,
  175,
  185,
  217,
  222,
  362,
  391,
  465,
  515,
  544,
  818,
  868,
  35,
  44,
  122,
  235,
  345,
  415,
  479,
  569,
  575,
  740,
  765,
  867,
  967,
  78,
  107,
  265,
  358,
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  331,
  346,
  844,
  852,
  7,
  216,
  248,
  548,
  637,
  733,
  788,
  810,
  909,
  151,
  205,
  248,
  297,
  381,
  501,
  589,
  601,
  610,
  693,
  851,
  211,
  379,
  508,
  770,
  955,
  17,
  216,
  372,
  471,
  804,
  838,
  934,
  977,
  16,
  119,
  332,
  338,
  478,
  628,
  803,
  911,
  8,
  132,
  144,
  169,
  192,
  713,
  748,
  808,
  824,
  13,
  19,
  31,
  78,
  94,
  513,
  561,
  587,
  825,
  953,
  248,
  254,
  470,
  520,
  594,
  634,
  636,
  647,
  830,
  862,
  869,
  17,
  37,
  62,
  138,
  270,
  337,
  449,
  474,
  540,
  566,
  583,
  721,
  929,
  935,
  954,
  221,
  273,
  315,
  397,
  447,
  641,
  725,
  830,
  885,
  928,
  7,
  175,
  188,
  464,
  482,
  493,
  519,
  612,
  615,
  666,
  758,
  807,
  915,
  70,
  133,
  350,
  438,
  479,
  522,
  564,
  893,
  120,
  273,
  384,
  424,
  446,
  447,
  467,
  585,
  633,
  792,
  948,
  997,
  7,
  51,
  151,
  197,
  232,
  348,
  581,
  596,
  628,
  833,
  890,
  32,
  96,
  265,
  272,
  387,
  691,
  694,
  17,
  322,
  369,
  457,
  499,
  611,
  735,
  813,
  885,
  72,
  84,
  130,
  210,
  228,
  334,
  349,
  396,
  443,
  483,
  498,
  508,
  509,
  762,
  105,
  127,
  157,
  198,
  206,
  286,
  298,
  371,
  380,
  516,
  698,
  738,
  837,
  840,
  946,
  982,
  359,
  436,
  687,
  802,
  805,
  950,
  112,
  113,
  141,
  282,
  290,
  524,
  527,
  624,
  642,
  762,
  840,
  858,
  997,
  30,
  257,
  465,
  573,
  605,
  661,
  752,
  783,
  795,
  880,
  907,
  8,
  101,
  145,
  253,
  375,
  459,
  556,
  559,
  584,
  748,
  999,
  50,
  180,
  388,
  638,
  902,
  122,
  192,
  405,
  468,
  486,
  562,
  604,
  841,
  844,
  134,
  197,
  381,
  382,
  414,
  430,
  431,
  655,
  666,
  807,
  958,
  81,
  210,
  496,
  538,
  724,
  903,
  947,
  51,
  118,
  243,
  326,
  537,
  597,
  836,
  966,
  11,
  139,
  147,
  204,
  214,
  269,
  288,
  290,
  304,
  307,
  334,
  451,
  575,
  600,
  661,
  775,
  800,
  969,
  986,
  64,
  206,
  269,
  403,
  461,
  508,
  548,
  581,
  596,
  692,
  777,
  124,
  232,
  312,
  322,
  447,
  498,
  526,
  543,
  656,
  670,
  712,
  751,
  907,
  923,
  71,
  94,
  114,
  148,
  201,
  249,
  293,
  296,
  331,
  336,
  505,
  607,
  768,
  933,
  217,
  260,
  296,
  302,
  311,
  581,
  625,
  655,
  781,
  892,
  926,
  23,
  43,
  100,
  156,
  273,
  337,
  572,
  673,
  741,
  980,
  52,
  156,
  164,
  336,
  373,
  400,
  470,
  951,
  20,
  30,
  73,
  179,
  351,
  566,
  636,
  872,
  883,
  944,
  11,
  62,
  460,
  482,
  486,
  495,
  512,
  651,
  868,
  917,
  997,
  16,
  74,
  417,
  496,
  590,
  639,
  692,
  778,
  781,
  855,
  928,
  930,
  259,
  275,
  477,
  637,
  748,
  807,
  957,
  999,
  38,
  184,
  260,
  266,
  268,
  323,
  391,
  598,
  628,
  881,
  947,
  54,
  62,
  219,
  270,
  471,
  473,
  491,
  673,
  859,
  892,
  947,
  72,
  218,
  309,
  331,
  372,
  573,
  741,
  822,
  825,
  966,
  48,
  200,
  205,
  237,
  261,
  265,
  338,
  353,
  666,
  928,
  967,
  53,
  74,
  259,
  284,
  507,
  615,
  886,
  905,
  955,
  10,
  21,
  44,
  406,
  460,
  684,
  782,
  816,
  826,
  907,
  34,
  189,
  260,
  332,
  356,
  444,
  460,
  758,
  781,
  838,
  842,
  905,
  967,
  6,
  7,
  169,
  220,
  295,
  384,
  399,
  442,
  739,
  922,
  969,
  286,
  300,
  401,
  460,
  503,
  659,
  686,
  727,
  749,
  785,
  974,
  993,
  998,
  183,
  210,
  328,
  450,
  453,
  480,
  496,
  517,
  525,
  549,
  635,
  716,
  732,
  748,
  749,
  832,
  959,
  95,
  107,
  121,
  258,
  326,
  416,
  588,
  654,
  753,
  831,
  34,
  83,
  101,
  181,
  224,
  552,
  623,
  671,
  866,
  983,
  997,
  104,
  129,
  143,
  198,
  213,
  420,
  438,
  612,
  674,
  910,
  943,
  210,
  212,
  218,
  321,
  330,
  455,
  692,
  794,
  839,
  960,
  965,
  17,
  101,
  124,
  395,
  476,
  513,
  514,
  566,
  692,
  846,
  856,
  859,
  862,
  908,
  920,
  947,
  958,
  8,
  200,
  373,
  462,
  556,
  739,
  796,
  932,
  951,
  958,
  44,
  56,
  186,
  262,
  310,
  355,
  380,
  470,
  593,
  714,
  906,
  964,
  989,
  65,
  114,
  195,
  306,
  307,
  355,
  403,
  469,
  513,
  654,
  685,
  800,
  812,
  816,
  825,
  843,
  925,
  3,
  328,
  425,
  486,
  730,
  773,
  789,
  824,
  943,
  966,
  967,
  981,
  984,
  83,
  156,
  311,
  439,
  545,
  565,
  650,
  682,
  769,
  299,
  341,
  409,
  782,
  943,
  5,
  52,
  57,
  123,
  146,
  175,
  409,
  443,
  532,
  989,
  120,
  158,
  430,
  436,
  449,
  640,
  659,
  734,
  749,
  834,
  882,
  911,
  952,
  22,
  226,
  442,
  591,
  879,
  51,
  69,
  86,
  97,
  178,
  263,
  316,
  425,
  534,
  554,
  565,
  888,
  988,
  991,
  24,
  352,
  511,
  522,
  555,
  570,
  603,
  696,
  887,
  960,
  39,
  133,
  260,
  401,
  465,
  526,
  609,
  732,
  131,
  206,
  305,
  669,
  809,
  877,
  986,
  439,
  520,
  567,
  588,
  617,
  712,
  891,
  998,
  274,
  358,
  425,
  495,
  715,
  872,
  918,
  923,
  951,
  980,
  983,
  119,
  123,
  316,
  324,
  349,
  644,
  705,
  718,
  769,
  781,
  795,
  884,
  110,
  133,
  140,
  152,
  157,
  495,
  569,
  608,
  629,
  803,
  827,
  909,
  942,
  9,
  230,
  268,
  423,
  626,
  707,
  724,
  748,
  828,
  996,
  274,
  308,
  436,
  722,
  879,
  213,
  259,
  324,
  329,
  377,
  534,
  588,
  827,
  896,
  149,
  261,
  591,
  597,
  785,
  813,
  883,
  920,
  996,
  10,
  64,
  237,
  417,
  535,
  686,
  709,
  717,
  744,
  41,
  67,
  260,
  370,
  405,
  407,
  520,
  632,
  893,
  955,
  127,
  250,
  336,
  354,
  388,
  474,
  591,
  703,
  805,
  811,
  833,
  871,
  881,
  991,
  994,
  17,
  91,
  113,
  122,
  300,
  301,
  463,
  716,
  741,
  776,
  784,
  906,
  994,
  33,
  57,
  206,
  448,
  520,
  612,
  769,
  834,
  282,
  393,
  441,
  461,
  503,
  796,
  72,
  206,
  304,
  381,
  565,
  723,
  114,
  121,
  130,
  259,
  346,
  386,
  432,
  538,
  575,
  595,
  855,
  945
};
const double x[1000] = {
  602,
  730,
  528,
  886,
  890,
  755,
  124,
  435,
  24,
  245,
  112,
  144,
  171,
  746,
  547,
  172,
  905,
  97,
  70,
  133,
  117,
  951,
  783,
  271,
  174,
  263,
  769,
  889,
  920,
  698,
  644,
  138,
  34,
  866,
  831,
  249,
  611,
  672,
  502,
  450,
  225,
  557,
  793,
  244,
  336,
  942,
  604,
  135,
  507,
  328,
  36,
  299,
  769,
  323,
  957,
  171,
  455,
  627,
  701,
  624,
  383,
  354,
  675,
  971,
  562,
  945,
  354,
  90,
  495,
  269,
  684,
  468,
  832,
  38,
  189,
  103,
  509,
  754,
  85,
  70,
  727,
  897,
  441,
  745,
  443,
  561,
  23,
  796,
  104,
  178,
  388,
  178,
  663,
  652,
  533,
  738,
  423,
  500,
  390,
  567,
  834,
  806,
  97,
  517,
  352,
  636,
  158,
  839,
  822,
  68,
  707,
  838,
  778,
  15,
  201,
  364,
  397,
  166,
  372,
  39,
  525,
  360,
  596,
  664,
  606,
  182,
  684,
  147,
  941,
  695,
  815,
  721,
  377,
  215,
  386,
  265,
  598,
  890,
  241,
  302,
  423,
  623,
  610,
  26,
  311,
  887,
  496,
  968,
  549,
  581,
  421,
  638,
  154,
  471,
  768,
  953,
  7,
  906,
  894,
  155,
  687,
  813,
  376,
  463,
  815,
  436,
  817,
  5,
  366,
  412,
  435,
  825,
  437,
  614,
  437,
  14,
  492,
  117,
  610,
  0,
  837,
  665,
  464,
  847,
  513,
  606,
  532,
  503,
  566,
  270,
  559,
  509,
  634,
  339,
  535,
  708,
  663,
  1,
  837,
  508,
  499,
  216,
  758,
  36,
  242,
  351,
  432,
  439,
  562,
  307,
  643,
  498,
  659,
  16,
  265,
  653,
  105,
  527,
  595,
  448,
  832,
  381,
  714,
  533,
  178,
  644,
  455,
  667,
  7,
  378,
  639,
  19,
  50,
  415,
  591,
  827,
  956,
  69,
  712,
  767,
  368,
  552,
  230,
  288,
  146,
  676,
  651,
  333,
  284,
  782,
  283,
  774,
  791,
  451,
  795,
  991,
  618,
  620,
  547,
  769,
  226,
  563,
  117,
  524,
  287,
  615,
  322,
  41,
  582,
  156,
  664,
  261,
  368,
  702,
  25,
  439,
  382,
  123,
  682,
  970,
  511,
  928,
  870,
  453,
  865,
  724,
  255,
  504,
  567,
  105,
  465,
  146,
  349,
  616,
  419,
  389,
  629,
  964,
  482,
  483,
  252,
  183,
  300,
  578,
  255,
  825,
  702,
  650,
  468,
  808,
  939,
  360,
  830,
  281,
  969,
  139,
  488,
  603,
  449,
  731,
  941,
  172,
  643,
  569,
  90,
  966,
  468,
  818,
  249,
  649,
  661,
  661,
  955,
  52,
  17,
  364,
  472,
  854,
  154,
  543,
  110,
  327,
  905,
  715,
  940,
  612,
  248,
  634,
  690,
  326,
  622,
  52,
  935,
  244,
  406,
  604,
  351,
  303,
  268,
  717,
  247,
  475,
  718,
  835,
  885,
  534,
  842,
  942,
  929,
  713,
  786,
  72,
  122,
  443,
  64,
  512,
  38,
  189,
  552,
  935,
  778,
  832,
  569,
  144,
  810,
  634,
  399,
  261,
  918,
  728,
  648,
  340,
  730,
  358,
  496,
  928,
  344,
  929,
  572,
  876,
  667,
  933,
  584,
  122,
  739,
  978,
  37,
  250,
  192,
  113,
  763,
  214,
  852,
  365,
  638,
  570,
  82,
  861,
  448,
  649,
  813,
  950,
  843,
  154,
  527,
  12,
  953,
  153,
  311,
  177,
  490,
  754,
  973,
  511,
  777,
  649,
  605,
  311,
  539,
  133,
  245,
  940,
  717,
  851,
  189,
  905,
  410,
  214,
  170,
  983,
  998,
  404,
  599,
  843,
  41,
  955,
  505,
  916,
  947,
  851,
  397,
  194,
  288,
  781,
  897,
  546,
  305,
  113,
  356,
  454,
  679,
  774,
  314,
  897,
  452,
  169,
  391,
  344,
  880,
  840,
  327,
  404,
  29,
  353,
  688,
  196,
  135,
  860,
  878,
  288,
  523,
  335,
  1,
  680,
  923,
  480,
  108,
  10,
  188,
  165,
  500,
  331,
  668,
  279,
  939,
  797,
  203,
  925,
  768,
  310,
  453,
  213,
  909,
  769,
  136,
  93,
  501,
  926,
  249,
  888,
  591,
  628,
  317,
  668,
  364,
  375,
  951,
  432,
  217,
  765,
  469,
  458,
  25,
  330,
  279,
  734,
  995,
  187,
  150,
  739,
  179,
  551,
  844,
  920,
  871,
  906,
  397,
  540,
  376,
  123,
  233,
  19,
  227,
  109,
  158,
  20,
  11,
  899,
  462,
  655,
  837,
  756,
  930,
  580,
  304,
  655,
  419,
  695,
  319,
  496,
  856,
  575,
  700,
  223,
  793,
  462,
  666,
  274,
  967,
  650,
  287,
  521,
  69,
  898,
  684,
  759,
  31,
  373,
  515,
  56,
  966,
  971,
  836,
  950,
  94,
  647,
  948,
  766,
  988,
  556,
  458,
  415,
  46,
  741,
  519,
  186,
  393,
  409,
  658,
  349,
  833,
  339,
  61,
  250,
  49,
  63,
  503,
  21,
  951,
  809,
  391,
  242,
  739,
  823,
  9,
  548,
  876,
  431,
  920,
  451,
  967,
  291,
  529,
  37,
  133,
  656,
  240,
  981,
  223,
  167,
  458,
  624,
  473,
  570,
  942,
  260,
  808,
  16,
  792,
  699,
  537,
  84,
  906,
  429,
  728,
  320,
  785,
  301,
  9,
  679,
  882,
  98,
  431,
  223,
  920,
  173,
  895,
  605,
  68,
  698,
  696,
  987,
  855,
  191,
  657,
  533,
  478,
  321,
  846,
  921,
  490,
  278,
  145,
  500,
  274,
  974,
  505,
  33,
  936,
  691,
  922,
  140,
  846,
  951,
  745,
  893,
  803,
  316,
  689,
  960,
  509,
  518,
  911,
  121,
  12,
  477,
  702,
  94,
  521,
  751,
  840,
  492,
  666,
  922,
  714,
  43,
  683,
  871,
  531,
  774,
  137,
  914,
  745,
  722,
  78,
  398,
  384,
  536,
  365,
  245,
  807,
  925,
  201,
  917,
  368,
  214,
  246,
  143,
  388,
  937,
  483,
  480,
  793,
  415,
  835,
  554,
  514,
  838,
  655,
  837,
  481,
  483,
  777,
  447,
  963,
  596,
  248,
  819,
  696,
  540,
  163,
  333,
  589,
  863,
  603,
  835,
  952,
  253,
  329,
  552,
  207,
  684,
  593,
  618,
  742,
  53,
  90,
  27,
  955,
  217,
  955,
  20,
  520,
  221,
  316,
  45,
  948,
  552,
  110,
  594,
  774,
  517,
  880,
  32,
  575,
  852,
  463,
  685,
  10,
  58,
  945,
  572,
  875,
  633,
  942,
  880,
  426,
  283,
  491,
  848,
  491,
  280,
  412,
  1,
  819,
  199,
  190,
  577,
  488,
  936,
  678,
  79,
  317,
  408,
  689,
  353,
  889,
  294,
  561,
  501,
  411,
  554,
  321,
  193,
  748,
  309,
  110,
  454,
  33,
  28,
  193,
  166,
  804,
  710,
  581,
  70,
  726,
  805,
  673,
  751,
  147,
  793,
  395,
  151,
  129,
  143,
  610,
  700,
  590,
  577,
  814,
  104,
  990,
  56,
  254,
  816,
  278,
  108,
  765,
  31,
  208,
  804,
  730,
  960,
  323,
  152,
  202,
  449,
  238,
  907,
  532,
  618,
  377,
  295,
  625,
  252,
  383,
  345,
  46,
  934,
  908,
  851,
  304,
  235,
  623,
  808,
  363,
  80,
  373,
  858,
  839,
  385,
  426,
  727,
  615,
  675,
  860,
  602,
  623,
  780,
  246,
  22,
  681,
  623,
  293,
  421,
  908,
  419,
  811,
  631,
  155,
  139,
  861,
  262,
  789,
  344,
  507,
  14,
  445,
  995,
  316,
  74,
  32,
  239,
  932,
  586,
  167,
  578,
  555,
  8,
  720,
  804,
  18,
  185,
  637,
  185,
  21,
  121,
  993,
  457,
  0,
  911,
  330,
  214,
  343,
  600,
  720,
  645,
  542,
  991,
  704,
  261,
  481,
  242,
  949,
  909,
  745,
  799,
  644,
  858,
  132,
  886,
  194,
  886,
  695,
  912,
  980,
  956,
  51,
  885,
  410,
  88,
  578,
  636,
  698,
  636,
  532,
  579,
  389,
  124,
  386,
  54,
  616,
  203,
  838,
  732,
  152,
  775,
  749,
  373
};
const int ptr[1001] = {
  0,
  6,
  18,
  31,
  40,
  49,
  58,
  67,
  75,
  85,
  98,
  111,
  121,
  135,
  139,
  146,
  159,
  169,
  175,
  181,
  191,
  203,
  210,
  217,
  228,
  238,
  245,
  254,
  265,
  278,
  290,
  298,
  311,
  323,
  332,
  343,
  353,
  360,
  370,
  383,
  396,
  407,
  415,
  427,
  433,
  440,
  449,
  461,
  467,
  474,
  487,
  503,
  510,
  522,
  530,
  542,
  549,
  556,
  570,
  584,
  594,
  605,
  614,
  624,
  629,
  637,
  644,
  653,
  663,
  674,
  685,
  691,
  701,
  712,
  723,
  734,
  746,
  754,
  766,
  779,
  788,
  802,
  809,
  820,
  831,
  846,
  860,
  869,
  874,
  883,
  886,
  900,
  915,
  929,
  937,
  946,
  955,
  969,
  985,
  993,
  1004,
  1014,
  1026,
  1035,
  1040,
  1053,
  1064,
  1073,
  1078,
  1089,
  1097,
  1105,
  1108,
  1119,
  1131,
  1143,
  1156,
  1165,
  1175,
  1187,
  1196,
  1205,
  1209,
  1218,
  1230,
  1242,
  1253,
  1263,
  1277,
  1288,
  1306,
  1323,
  1331,
  1345,
  1355,
  1362,
  1372,
  1380,
  1388,
  1395,
  1412,
  1424,
  1428,
  1436,
  1443,
  1457,
  1473,
  1488,
  1498,
  1511,
  1520,
  1533,
  1543,
  1556,
  1567,
  1578,
  1590,
  1598,
  1609,
  1618,
  1627,
  1634,
  1638,
  1643,
  1649,
  1654,
  1660,
  1675,
  1688,
  1698,
  1712,
  1722,
  1730,
  1738,
  1746,
  1758,
  1765,
  1778,
  1787,
  1802,
  1814,
  1821,
  1833,
  1842,
  1851,
  1864,
  1877,
  1886,
  1890,
  1898,
  1904,
  1916,
  1931,
  1942,
  1953,
  1966,
  1975,
  1988,
  1999,
  2008,
  2021,
  2027,
  2036,
  2049,
  2058,
  2069,
  2078,
  2086,
  2099,
  2109,
  2115,
  2123,
  2133,
  2142,
  2155,
  2166,
  2175,
  2185,
  2191,
  2202,
  2215,
  2220,
  2234,
  2248,
  2260,
  2271,
  2277,
  2285,
  2297,
  2310,
  2318,
  2328,
  2337,
  2352,
  2358,
  2370,
  2378,
  2391,
  2397,
  2407,
  2413,
  2425,
  2434,
  2442,
  2452,
  2462,
  2476,
  2480,
  2487,
  2500,
  2512,
  2525,
  2533,
  2545,
  2552,
  2563,
  2576,
  2585,
  2591,
  2599,
  2608,
  2619,
  2629,
  2643,
  2658,
  2664,
  2675,
  2682,
  2696,
  2705,
  2715,
  2718,
  2736,
  2746,
  2765,
  2771,
  2787,
  2793,
  2802,
  2813,
  2826,
  2837,
  2849,
  2863,
  2870,
  2885,
  2895,
  2904,
  2914,
  2925,
  2931,
  2944,
  2949,
  2957,
  2973,
  2982,
  2995,
  3009,
  3025,
  3031,
  3046,
  3061,
  3069,
  3082,
  3089,
  3100,
  3106,
  3116,
  3119,
  3123,
  3130,
  3136,
  3144,
  3153,
  3162,
  3180,
  3185,
  3200,
  3205,
  3215,
  3225,
  3234,
  3246,
  3255,
  3266,
  3273,
  3283,
  3293,
  3303,
  3312,
  3320,
  3331,
  3342,
  3349,
  3357,
  3367,
  3372,
  3380,
  3387,
  3398,
  3405,
  3417,
  3425,
  3432,
  3443,
  3449,
  3456,
  3461,
  3471,
  3480,
  3491,
  3498,
  3521,
  3530,
  3539,
  3554,
  3562,
  3569,
  3579,
  3585,
  3597,
  3604,
  3613,
  3628,
  3646,
  3657,
  3673,
  3681,
  3691,
  3696,
  3709,
  3717,
  3731,
  3745,
  3756,
  3763,
  3769,
  3774,
  3786,
  3799,
  3810,
  3819,
  3827,
  3838,
  3854,
  3867,
  3876,
  3885,
  3902,
  3911,
  3926,
  3936,
  3948,
  3959,
  3970,
  3983,
  3991,
  4002,
  4009,
  4023,
  4032,
  4043,
  4058,
  4065,
  4078,
  4087,
  4099,
  4106,
  4114,
  4120,
  4132,
  4146,
  4155,
  4168,
  4177,
  4189,
  4199,
  4212,
  4219,
  4231,
  4241,
  4253,
  4260,
  4266,
  4278,
  4287,
  4303,
  4310,
  4322,
  4334,
  4344,
  4354,
  4368,
  4376,
  4383,
  4399,
  4408,
  4416,
  4431,
  4444,
  4458,
  4467,
  4474,
  4486,
  4495,
  4506,
  4515,
  4521,
  4536,
  4549,
  4564,
  4571,
  4580,
  4593,
  4602,
  4613,
  4618,
  4627,
  4635,
  4644,
  4659,
  4664,
  4675,
  4684,
  4690,
  4702,
  4713,
  4723,
  4735,
  4743,
  4751,
  4759,
  4768,
  4779,
  4790,
  4799,
  4811,
  4818,
  4823,
  4830,
  4838,
  4850,
  4861,
  4870,
  4878,
  4890,
  4897,
  4908,
  4916,
  4930,
  4939,
  4950,
  4959,
  4971,
  4977,
  4985,
  4996,
  4999,
  5003,
  5012,
  5018,
  5026,
  5041,
  5048,
  5058,
  5071,
  5081,
  5086,
  5094,
  5099,
  5109,
  5114,
  5127,
  5137,
  5147,
  5162,
  5172,
  5179,
  5187,
  5197,
  5209,
  5226,
  5231,
  5239,
  5248,
  5263,
  5270,
  5283,
  5293,
  5301,
  5308,
  5318,
  5327,
  5342,
  5349,
  5357,
  5367,
  5374,
  5381,
  5395,
  5406,
  5418,
  5428,
  5435,
  5440,
  5452,
  5464,
  5477,
  5490,
  5497,
  5504,
  5510,
  5518,
  5529,
  5542,
  5561,
  5579,
  5588,
  5599,
  5601,
  5609,
  5618,
  5627,
  5631,
  5640,
  5646,
  5654,
  5661,
  5672,
  5690,
  5699,
  5712,
  5723,
  5733,
  5742,
  5752,
  5759,
  5766,
  5776,
  5788,
  5799,
  5801,
  5813,
  5825,
  5829,
  5841,
  5846,
  5858,
  5867,
  5878,
  5892,
  5902,
  5910,
  5921,
  5933,
  5941,
  5957,
  5964,
  5975,
  5988,
  6000,
  6007,
  6019,
  6027,
  6036,
  6046,
  6055,
  6065,
  6080,
  6090,
  6098,
  6110,
  6122,
  6139,
  6151,
  6160,
  6168,
  6181,
  6190,
  6202,
  6209,
  6221,
  6228,
  6238,
  6249,
  6260,
  6266,
  6274,
  6289,
  6302,
  6310,
  6325,
  6334,
  6349,
  6367,
  6370,
  6382,
  6391,
  6399,
  6414,
  6423,
  6435,
  6442,
  6452,
  6461,
  6469,
  6479,
  6493,
  6502,
  6517,
  6524,
  6539,
  6549,
  6555,
  6561,
  6568,
  6575,
  6594,
  6605,
  6613,
  6620,
  6626,
  6637,
  6643,
  6656,
  6669,
  6679,
  6687,
  6698,
  6706,
  6715,
  6730,
  6739,
  6746,
  6762,
  6768,
  6776,
  6785,
  6791,
  6798,
  6805,
  6818,
  6827,
  6836,
  6846,
  6853,
  6861,
  6877,
  6885,
  6894,
  6901,
  6912,
  6924,
  6937,
  6947,
  6951,
  6966,
  6975,
  6985,
  6996,
  7003,
  7019,
  7029,
  7037,
  7046,
  7053,
  7060,
  7068,
  7075,
  7081,
  7088,
  7094,
  7108,
  7117,
  7123,
  7139,
  7150,
  7162,
  7168,
  7182,
  7191,
  7203,
  7219,
  7222,
  7229,
  7243,
  7251,
  7260,
  7269,
  7279,
  7289,
  7294,
  7307,
  7321,
  7338,
  7349,
  7353,
  7361,
  7371,
  7379,
  7386,
  7397,
  7411,
  7422,
  7428,
  7437,
  7442,
  7452,
  7463,
  7474,
  7483,
  7491,
  7499,
  7514,
  7523,
  7536,
  7542,
  7549,
  7556,
  7568,
  7577,
  7586,
  7597,
  7609,
  7623,
  7633,
  7645,
  7658,
  7664,
  7677,
  7694,
  7703,
  7718,
  7727,
  7736,
  7749,
  7758,
  7768,
  7775,
  7782,
  7790,
  7803,
  7812,
  7823,
  7833,
  7842,
  7859,
  7870,
  7879,
  7891,
  7901,
  7912,
  7921,
  7928,
  7935,
  7943,
  7958,
  7965,
  7972,
  7984,
  7991,
  7997,
  8010,
  8020,
  8033,
  8041,
  8048,
  8059,
  8069,
  8080,
  8088,
  8097,
  8108,
  8113,
  8119,
  8128,
  8135,
  8148,
  8163,
  8172,
  8182,
  8194,
  8203,
  8214,
  8223,
  8237,
  8246,
  8252,
  8264,
  8269,
  8282,
  8293,
  8305,
  8317,
  8330,
  8336,
  8347,
  8354,
  8364,
  8376,
  8383,
  8398,
  8406,
  8414,
  8429,
  8443,
  8460,
  8467,
  8475,
  8484,
  8493,
  8503,
  8510,
  8518,
  8527,
  8535,
  8544,
  8548,
  8555,
  8561,
  8571,
  8578,
  8590,
  8599,
  8603,
  8614,
  8621,
  8628,
  8638,
  8644,
  8654,
  8664,
  8675,
  8688,
  8698,
  8705,
  8711,
  8721,
  8729,
  8739,
  8754,
  8770,
  8775,
  8792,
  8802,
  8812,
  8824,
  8829,
  8838,
  8847,
  8858,
  8869,
  8878,
  8889,
  8906,
  8911,
  8916,
  8928,
  8939,
  8950,
  8957,
  8969,
  8980,
  8988,
  8992,
  9005,
  9014,
  9024,
  9032,
  9048,
  9060,
  9069,
  9079,
  9086,
  9098,
  9112,
  9123,
  9135,
  9143,
  9152,
  9163,
  9168,
  9176,
  9184,
  9193,
  9203,
  9214,
  9229,
  9239,
  9252,
  9260,
  9272,
  9283,
  9290,
  9299,
  9313,
  9329,
  9335,
  9348,
  9359,
  9370,
  9375,
  9384,
  9395,
  9402,
  9410,
  9429,
  9440,
  9454,
  9468,
  9479,
  9489,
  9497,
  9507,
  9518,
  9530,
  9538,
  9549,
  9560,
  9570,
  9581,
  9590,
  9600,
  9613,
  9624,
  9637,
  9654,
  9664,
  9675,
  9686,
  9697,
  9714,
  9724,
  9737,
  9754,
  9767,
  9776,
  9781,
  9791,
  9804,
  9809,
  9823,
  9833,
  9841,
  9848,
  9856,
  9867,
  9879,
  9892,
  9902,
  9907,
  9916,
  9925,
  9934,
  9944,
  9959,
  9972,
  9980,
  9986,
  9992,
  10004
};
const double verify_data[1000] = {
  1971101,
  3601995,
  3608374,
  3068439,
  2756891,
  1644445,
  2326970,
  3571797,
  2167311,
  3272467,
  5257490,
  2287052,
  5507394,
  1707471,
  1181529,
  2596954,
  2999820,
  1456597,
  1755714,
  2783599,
  2224880,
  953747,
  1863442,
  2375479,
  3838149,
  1472958,
  2613759,
  1412651,
  2454897,
  4139599,
  1540527,
  2373885,
  2371153,
  2496043,
  2946006,
  3041837,
  2102841,
  3413598,
  3937131,
  3428786,
  2323528,
  1657458,
  3358521,
  1821261,
  937257,
  2638848,
  3351703,
  2436591,
  1387045,
  3372777,
  4422352,
  2696491,
  2775768,
  1711500,
  2463910,
  1906176,
  2655972,
  2176802,
  4025605,
  1836921,
  2902963,
  1950818,
  2553243,
  2012524,
  2449182,
  1632320,
  2628093,
  1093587,
  3089207,
  3020390,
  1485696,
  1932818,
  3334949,
  1610563,
  2076427,
  3114683,
  1548840,
  3339439,
  3335032,
  1366398,
  1685659,
  1668385,
  2510712,
  2871270,
  3270369,
  4311377,
  1982006,
  1326681,
  1381634,
  398901,
  3333661,
  3352243,
  2878790,
  1577319,
  2415255,
  1191188,
  3219765,
  3467850,
  1940862,
  2056258,
  1786527,
  2278347,
  2077897,
  1457888,
  3707208,
  1405999,
  952210,
  1600564,
  2343319,
  1781556,
  2474389,
  522450,
  3674982,
  3619187,
  3211390,
  3586103,
  1475431,
  3546147,
  3698208,
  2049193,
  1979189,
  1111515,
  2790498,
  3439083,
  4279066,
  2774436,
  2077245,
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